It is currently 11 Dec 2017, 08:29

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is 7^7/7^x an integer?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 15 Feb 2010
Posts: 11

Kudos [?]: 13 [0], given: 0

### Show Tags

19 Mar 2010, 19:35
4
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

50% (00:48) correct 50% (00:38) wrong based on 224 sessions

### HideShow timer Statistics

Is $$\frac{7^7}{7^x}$$ an integer?

(1) $$0\leq{x}\leq{7}$$
(2) $$|x|=x^2$$

(C) 2008 GMAT Club - m04#26

[Reveal] Spoiler:
Statement (1) by itself is insufficient. S1 says that x can be between 0 and 7, so it can be an integer or any fraction.

Statement (2) by itself is sufficient. S2 implies that x is one of (-1, 0, 1). .

WHY CAN THIS BE AN INTEGER OR ANY FRACTION, ISN'T IT ANY INTEGER ALL THE WAY. BECAUSE THE LEAST WHEN X= 7 IS 1 AND X=0 IS 7 * 7*7*7*7*7*7
[Reveal] Spoiler: OA

Kudos [?]: 13 [0], given: 0

Manager
Joined: 13 Dec 2009
Posts: 248

Kudos [?]: 265 [0], given: 13

Re: Is 7^7/7^x an integer? [#permalink]

### Show Tags

20 Mar 2010, 07:53
aramjung wrote:
Is $$\frac{7^7}{7^x}$$ an integer?

(1) $$0\leq{x}\leq{7}$$
(2) $$|x|=x^2$$

stmt1: x can be fraction between 0 to 7 so insuff.
stmt2: |x| = x^2
-x = x^2 => x(x+1) = 0 => x = 0 or x = -1
or
x = x^2 => x(x-1) = 0 => x = 0 or x = 1
in any of the three cases 0, 1 , -1 it is going ot be an integer to sufficient.
it cannot be fraction all the way, take for example x = 1/2 it is between 0 to 7 but 7^7/7^1/2 is not an integer
_________________

My debrief: done-and-dusted-730-q49-v40

Kudos [?]: 265 [0], given: 13

Intern
Joined: 19 Mar 2010
Posts: 10

Kudos [?]: 4 [0], given: 3

Location: San Diego, CA
Schools: UCLA Anderson
Re: Is 7^7/7^x an integer? [#permalink]

### Show Tags

20 Mar 2010, 10:37
S1. It is not specified that x is an integer. Using a value such as x=3.5 in the original function will result in a non-integer. Insufficient.
S2. x can only be equal to -1, 0. or 1. Using these values in the original function will always result in an integer. Sufficient.

Kudos [?]: 4 [0], given: 3

Senior Manager
Status: Can't give up
Joined: 20 Dec 2009
Posts: 305

Kudos [?]: 36 [0], given: 35

Re: Is 7^7/7^x an integer? [#permalink]

### Show Tags

20 Mar 2010, 11:08
1.) x can be any value from 0-7 including decimals. so this is Insuff

2.) using B x= -1, 0, 1, -2, 2.....x is an integer.

Hence B

Kudos [?]: 36 [0], given: 35

Non-Human User
Joined: 09 Sep 2013
Posts: 14945

Kudos [?]: 287 [0], given: 0

Re: Is 7^7/7^x an integer? [#permalink]

### Show Tags

26 Aug 2015, 13:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 287 [0], given: 0

Intern
Joined: 20 Apr 2015
Posts: 5

Kudos [?]: [0], given: 26

Re: Is 7^7/7^x an integer? [#permalink]

### Show Tags

07 Oct 2015, 03:41
stmt1: x can be fraction between 0 to 7 so insuff.
stmt2: |x| = x^2
-x = x^2 => x(x+1) = 0 => x = 0 or x = -1
or
x = x^2 => x(x-1) = 0 => x = 0 or x = 1
in any of the three cases 0, 1 , -1 it is going ot be an integer to sufficient.

hii please tell me how do we get just those 3 values for x.

Kudos [?]: [0], given: 26

Math Expert
Joined: 02 Sep 2009
Posts: 42545

Kudos [?]: 135229 [0], given: 12674

Re: Is 7^7/7^x an integer? [#permalink]

### Show Tags

07 Oct 2015, 05:35
shreeya wrote:
stmt1: x can be fraction between 0 to 7 so insuff.
stmt2: |x| = x^2
-x = x^2 => x(x+1) = 0 => x = 0 or x = -1
or
x = x^2 => x(x-1) = 0 => x = 0 or x = 1
in any of the three cases 0, 1 , -1 it is going ot be an integer to sufficient.

hii please tell me how do we get just those 3 values for x.

Square $$|x| = x^2$$:

$$x^2 = x^4$$;

$$x^2 - x^4 = 0$$;

$$x^2(1 - x^2) = 0$$;

$$x^2(1 - x)(1 + x) = 0$$;

$$x = 0$$, $$x = 1$$, or $$x = -1$$.

Hope it's clear.
_________________

Kudos [?]: 135229 [0], given: 12674

Intern
Joined: 20 Apr 2015
Posts: 5

Kudos [?]: [0], given: 26

Re: Is 7^7/7^x an integer? [#permalink]

### Show Tags

07 Oct 2015, 07:29
yes .. thanks

Kudos [?]: [0], given: 26

Re: Is 7^7/7^x an integer?   [#permalink] 07 Oct 2015, 07:29
Display posts from previous: Sort by